%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:42:48 PM UTC 2026
% Result : Theorem 0.23s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n005.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 02:26:18 UTC 2026
% 0.18/0.49 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.23/0.60 % Refutation found
% 0.23/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.60 % SZS output start CNFRefutation for theBenchmark
% 0.23/0.60 fof(f1,axiom,(
% 0.23/0.60 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f2,axiom,(
% 0.23/0.60 (! [A] :( empty(A)=> function(A) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f3,axiom,(
% 0.23/0.60 (! [A] :( empty(A)=> relation(A) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f4,axiom,(
% 0.23/0.60 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f5,axiom,(
% 0.23/0.60 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f6,axiom,(
% 0.23/0.60 (! [A] : succ(A) = set_union2(A,singleton(A)) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f7,axiom,(
% 0.23/0.60 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f8,axiom,(
% 0.23/0.60 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f10,axiom,(
% 0.23/0.60 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f19,axiom,(
% 0.23/0.60 (? [A] :( empty(A)& relation(A) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f20,axiom,(
% 0.23/0.60 (? [A] : empty(A) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f21,axiom,(
% 0.23/0.60 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f28,conjecture,(
% 0.23/0.60 (! [A,B] :( in(A,succ(B))<=> ( in(A,B)| A = B ) ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f29,negated_conjecture,(
% 0.23/0.60 ~((! [A,B] :( in(A,succ(B))<=> ( in(A,B)| A = B ) ) ))),
% 0.23/0.60 inference(negated_conjecture,[status(cth)],[f28])).
% 0.23/0.60 fof(f30,axiom,(
% 0.23/0.60 (! [A] : set_union2(A,empty_set) = A )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f33,axiom,(
% 0.23/0.60 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.23/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.60 fof(f36,plain,(
% 0.23/0.60 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.23/0.60 fof(f37,plain,(
% 0.23/0.60 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f36])).
% 0.23/0.60 fof(f38,plain,(
% 0.23/0.60 ![A]: (~empty(A)|function(A))),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.23/0.60 fof(f39,plain,(
% 0.23/0.60 ![X0]: (~empty(X0)|function(X0))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f38])).
% 0.23/0.60 fof(f40,plain,(
% 0.23/0.60 ![A]: (~empty(A)|relation(A))),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.23/0.60 fof(f41,plain,(
% 0.23/0.60 ![X0]: (~empty(X0)|relation(X0))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f40])).
% 0.23/0.60 fof(f42,plain,(
% 0.23/0.60 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.23/0.60 fof(f45,plain,(
% 0.23/0.60 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f42])).
% 0.23/0.60 fof(f46,plain,(
% 0.23/0.60 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f5])).
% 0.23/0.60 fof(f47,plain,(
% 0.23/0.60 ![X0]: (succ(X0)=set_union2(X0,singleton(X0)))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f6])).
% 0.23/0.60 fof(f48,plain,(
% 0.23/0.60 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.23/0.60 inference(NNF_transformation,[status(thm)],[f7])).
% 0.23/0.60 fof(f49,plain,(
% 0.23/0.60 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.23/0.60 inference(miniscoping,[status(thm)],[f48])).
% 0.23/0.60 fof(f50,plain,(
% 0.23/0.60 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK0_skl(B,A),B)|~sK0_skl(B,A)=A)&(in(sK0_skl(B,A),B)|sK0_skl(B,A)=A))))),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f49])).
% 0.23/0.60 fof(f51,plain,(
% 0.23/0.60 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f50])).
% 0.23/0.60 fof(f52,plain,(
% 0.23/0.60 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f50])).
% 0.23/0.60 fof(f55,plain,(
% 0.23/0.60 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.23/0.60 inference(NNF_transformation,[status(thm)],[f8])).
% 0.23/0.60 fof(f56,plain,(
% 0.23/0.60 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.23/0.60 inference(miniscoping,[status(thm)],[f55])).
% 0.23/0.60 fof(f57,plain,(
% 0.23/0.60 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sK1_skl(C,B,A),C)|(~in(sK1_skl(C,B,A),A)&~in(sK1_skl(C,B,A),B)))&(in(sK1_skl(C,B,A),C)|(in(sK1_skl(C,B,A),A)|in(sK1_skl(C,B,A),B))))))),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f56])).
% 0.23/0.60 fof(f58,plain,(
% 0.23/0.60 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|~in(X3,X0)|in(X3,X1)|in(X3,X2))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f57])).
% 0.23/0.60 fof(f59,plain,(
% 0.23/0.60 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f57])).
% 0.23/0.60 fof(f60,plain,(
% 0.23/0.60 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X2))),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f57])).
% 0.23/0.60 fof(f66,plain,(
% 0.23/0.60 empty(empty_set)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f10])).
% 0.23/0.60 fof(f86,plain,(
% 0.23/0.60 (empty(sK4_skl)&relation(sK4_skl))),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f19])).
% 0.23/0.60 fof(f87,plain,(
% 0.23/0.60 empty(sK4_skl)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f86])).
% 0.23/0.60 fof(f89,plain,(
% 0.23/0.60 empty(sK5_skl)),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f20])).
% 0.23/0.60 fof(f90,plain,(
% 0.23/0.60 empty(sK5_skl)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f89])).
% 0.23/0.60 fof(f91,plain,(
% 0.23/0.60 ((relation(sK6_skl)&empty(sK6_skl))&function(sK6_skl))),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f21])).
% 0.23/0.60 fof(f93,plain,(
% 0.23/0.60 empty(sK6_skl)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f91])).
% 0.23/0.60 fof(f94,plain,(
% 0.23/0.60 function(sK6_skl)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f91])).
% 0.23/0.60 fof(f115,plain,(
% 0.23/0.60 (?[A,B]: (in(A,succ(B))<~>(in(A,B)|A=B)))),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.23/0.60 fof(f116,plain,(
% 0.23/0.60 ?[A,B]: ((in(A,succ(B))|(in(A,B)|A=B))&(~in(A,succ(B))|(~in(A,B)&~A=B)))),
% 0.23/0.60 inference(NNF_transformation,[status(thm)],[f115])).
% 0.23/0.60 fof(f117,plain,(
% 0.23/0.60 ((in(sK13_skl,succ(sK14_skl))|(in(sK13_skl,sK14_skl)|sK13_skl=sK14_skl))&(~in(sK13_skl,succ(sK14_skl))|(~in(sK13_skl,sK14_skl)&~sK13_skl=sK14_skl)))),
% 0.23/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f116])).
% 0.23/0.60 fof(f118,plain,(
% 0.23/0.60 in(sK13_skl,succ(sK14_skl))|in(sK13_skl,sK14_skl)|sK13_skl=sK14_skl),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f117])).
% 0.23/0.60 fof(f119,plain,(
% 0.23/0.60 ~in(sK13_skl,succ(sK14_skl))|~in(sK13_skl,sK14_skl)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f117])).
% 0.23/0.60 fof(f120,plain,(
% 0.23/0.60 ~in(sK13_skl,succ(sK14_skl))|~sK13_skl=sK14_skl),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f117])).
% 0.23/0.60 fof(f121,plain,(
% 0.23/0.60 ![X0]: (set_union2(X0,empty_set)=X0)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f30])).
% 0.23/0.60 fof(f126,plain,(
% 0.23/0.60 ![A]: (~empty(A)|A=empty_set)),
% 0.23/0.60 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.23/0.60 fof(f127,plain,(
% 0.23/0.60 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.23/0.60 inference(cnf_transformation,[status(thm)],[f126])).
% 0.23/0.60 fof(f134,definition,(
% 0.23/0.60 sQ0_spl <=> (in(sK13_skl,succ(sK14_skl)))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f135,plain,(
% 0.23/0.60 in(sK13_skl,succ(sK14_skl))|~sQ0_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f134])).
% 0.23/0.60 fof(f136,plain,(
% 0.23/0.60 ~in(sK13_skl,succ(sK14_skl))|sQ0_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f134])).
% 0.23/0.60 fof(f137,definition,(
% 0.23/0.60 sQ1_spl <=> (in(sK13_skl,sK14_skl))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f138,plain,(
% 0.23/0.60 in(sK13_skl,sK14_skl)|~sQ1_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f137])).
% 0.23/0.60 fof(f140,definition,(
% 0.23/0.60 sQ2_spl <=> (sK13_skl=sK14_skl)),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f141,plain,(
% 0.23/0.60 sK13_skl=sK14_skl|~sQ2_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f140])).
% 0.23/0.60 fof(f143,plain,(
% 0.23/0.60 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f118,f134,f137,f140])).
% 0.23/0.60 fof(f144,plain,(
% 0.23/0.60 ~sQ0_spl|~sQ1_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f119,f134,f137])).
% 0.23/0.60 fof(f145,plain,(
% 0.23/0.60 ~sQ0_spl|~sQ2_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f120,f134,f140])).
% 0.23/0.60 fof(f146,plain,(
% 0.23/0.60 ![X0,X1]: (~X0=singleton(X1)|in(X1,X0))),
% 0.23/0.60 inference(destructive_equality_resolution,[status(thm)],[f52])).
% 0.23/0.60 fof(f148,plain,(
% 0.23/0.60 function(empty_set)),
% 0.23/0.60 inference(resolution,[status(thm)],[f66,f39])).
% 0.23/0.60 fof(f149,plain,(
% 0.23/0.60 function(sK4_skl)),
% 0.23/0.60 inference(resolution,[status(thm)],[f87,f39])).
% 0.23/0.60 fof(f150,plain,(
% 0.23/0.60 function(sK5_skl)),
% 0.23/0.60 inference(resolution,[status(thm)],[f90,f39])).
% 0.23/0.60 fof(f154,plain,(
% 0.23/0.60 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.23/0.60 inference(forward_subsumption_resolution,[status(thm)],[f45,f41])).
% 0.23/0.60 fof(f165,plain,(
% 0.23/0.60 ~empty(sK6_skl)|one_to_one(sK6_skl)),
% 0.23/0.60 inference(resolution,[status(thm)],[f94,f154])).
% 0.23/0.60 fof(f166,definition,(
% 0.23/0.60 sQ5_spl <=> (empty(sK6_skl))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f168,plain,(
% 0.23/0.60 ~empty(sK6_skl)|sQ5_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f166])).
% 0.23/0.60 fof(f169,definition,(
% 0.23/0.60 sQ6_spl <=> (one_to_one(sK6_skl))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f172,plain,(
% 0.23/0.60 ~sQ5_spl|sQ6_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f165,f166,f169])).
% 0.23/0.60 fof(f173,plain,(
% 0.23/0.60 $false|sQ5_spl),
% 0.23/0.60 inference(forward_subsumption_resolution,[status(thm)],[f168,f93])).
% 0.23/0.60 fof(f174,plain,(
% 0.23/0.60 sQ5_spl),
% 0.23/0.60 inference(contradiction_clause,[status(thm)],[f173])).
% 0.23/0.60 fof(f199,plain,(
% 0.23/0.60 ~empty(empty_set)|one_to_one(empty_set)),
% 0.23/0.60 inference(resolution,[status(thm)],[f148,f154])).
% 0.23/0.60 fof(f200,definition,(
% 0.23/0.60 sQ13_spl <=> (empty(empty_set))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f202,plain,(
% 0.23/0.60 ~empty(empty_set)|sQ13_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f200])).
% 0.23/0.60 fof(f203,definition,(
% 0.23/0.60 sQ14_spl <=> (one_to_one(empty_set))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f206,plain,(
% 0.23/0.60 ~sQ13_spl|sQ14_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f199,f200,f203])).
% 0.23/0.60 fof(f207,plain,(
% 0.23/0.60 $false|sQ13_spl),
% 0.23/0.60 inference(forward_subsumption_resolution,[status(thm)],[f202,f66])).
% 0.23/0.60 fof(f208,plain,(
% 0.23/0.60 sQ13_spl),
% 0.23/0.60 inference(contradiction_clause,[status(thm)],[f207])).
% 0.23/0.60 fof(f209,plain,(
% 0.23/0.60 ~empty(sK4_skl)|one_to_one(sK4_skl)),
% 0.23/0.60 inference(resolution,[status(thm)],[f149,f154])).
% 0.23/0.60 fof(f210,definition,(
% 0.23/0.60 sQ15_spl <=> (empty(sK4_skl))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f212,plain,(
% 0.23/0.60 ~empty(sK4_skl)|sQ15_spl),
% 0.23/0.60 inference(component_clause,[status(thm)],[f210])).
% 0.23/0.60 fof(f213,definition,(
% 0.23/0.60 sQ16_spl <=> (one_to_one(sK4_skl))),
% 0.23/0.60 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.23/0.60 fof(f216,plain,(
% 0.23/0.60 ~sQ15_spl|sQ16_spl),
% 0.23/0.60 inference(split_clause,[status(thm)],[f209,f210,f213])).
% 0.23/0.60 fof(f217,plain,(
% 0.23/0.60 $false|sQ15_spl),
% 0.23/0.60 inference(forward_subsumption_resolution,[status(thm)],[f212,f87])).
% 0.23/0.60 fof(f218,plain,(
% 0.23/0.60 sQ15_spl),
% 0.23/0.60 inference(contradiction_clause,[status(thm)],[f217])).
% 0.23/0.60 fof(f224,plain,(
% 0.23/0.60 ![X0]: (in(X0,singleton(X0)))),
% 0.23/0.60 inference(equality_resolution,[status(thm)],[f146])).
% 0.23/0.60 fof(f225,plain,(
% 0.23/0.60 ~empty(sK5_skl)|one_to_one(sK5_skl)),
% 0.23/0.60 inference(resolution,[status(thm)],[f150,f154])).
% 0.23/0.61 fof(f226,definition,(
% 0.23/0.61 sQ17_spl <=> (empty(sK5_skl))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f228,plain,(
% 0.23/0.61 ~empty(sK5_skl)|sQ17_spl),
% 0.23/0.61 inference(component_clause,[status(thm)],[f226])).
% 0.23/0.61 fof(f229,definition,(
% 0.23/0.61 sQ18_spl <=> (one_to_one(sK5_skl))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f232,plain,(
% 0.23/0.61 ~sQ17_spl|sQ18_spl),
% 0.23/0.61 inference(split_clause,[status(thm)],[f225,f226,f229])).
% 0.23/0.61 fof(f233,plain,(
% 0.23/0.61 $false|sQ17_spl),
% 0.23/0.61 inference(forward_subsumption_resolution,[status(thm)],[f228,f90])).
% 0.23/0.61 fof(f234,plain,(
% 0.23/0.61 sQ17_spl),
% 0.23/0.61 inference(contradiction_clause,[status(thm)],[f233])).
% 0.23/0.61 fof(f239,plain,(
% 0.23/0.61 ![X0]: (set_union2(empty_set,X0)=X0)),
% 0.23/0.61 inference(paramodulation,[status(thm)],[f46,f121])).
% 0.23/0.61 fof(f245,plain,(
% 0.23/0.61 sK6_skl=empty_set),
% 0.23/0.61 inference(resolution,[status(thm)],[f127,f93])).
% 0.23/0.61 fof(f271,plain,(
% 0.23/0.61 ![X0]: (set_union2(sK6_skl,X0)=X0)),
% 0.23/0.61 inference(forward_demodulation,[status(thm)],[f245,f239])).
% 0.23/0.61 fof(f273,plain,(
% 0.23/0.61 succ(sK6_skl)=singleton(sK6_skl)),
% 0.23/0.61 inference(paramodulation,[status(thm)],[f47,f271])).
% 0.23/0.61 fof(f303,plain,(
% 0.23/0.61 ![X0,X1]: (~in(X0,succ(X1))|in(X0,X1)|in(X0,singleton(X1)))),
% 0.23/0.61 inference(resolution,[status(thm)],[f58,f47])).
% 0.23/0.61 fof(f322,plain,(
% 0.23/0.61 ![X0,X1]: (in(X0,succ(X1))|~in(X0,X1))),
% 0.23/0.61 inference(resolution,[status(thm)],[f59,f47])).
% 0.23/0.61 fof(f342,plain,(
% 0.23/0.61 ![X0,X1]: (in(X0,succ(X1))|~in(X0,singleton(X1)))),
% 0.23/0.61 inference(resolution,[status(thm)],[f60,f47])).
% 0.23/0.61 fof(f358,plain,(
% 0.23/0.61 in(sK6_skl,succ(sK6_skl))),
% 0.23/0.61 inference(resolution,[status(thm)],[f273,f146])).
% 0.23/0.61 fof(f372,plain,(
% 0.23/0.61 ![X0]: (~succ(sK6_skl)=singleton(X0)|sK6_skl=X0)),
% 0.23/0.61 inference(resolution,[status(thm)],[f358,f51])).
% 0.23/0.61 fof(f374,plain,(
% 0.23/0.61 in(sK6_skl,sK6_skl)|in(sK6_skl,singleton(sK6_skl))),
% 0.23/0.61 inference(resolution,[status(thm)],[f303,f358])).
% 0.23/0.61 fof(f376,definition,(
% 0.23/0.61 sQ21_spl <=> (in(sK6_skl,sK6_skl))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f377,plain,(
% 0.23/0.61 in(sK6_skl,sK6_skl)|~sQ21_spl),
% 0.23/0.61 inference(component_clause,[status(thm)],[f376])).
% 0.23/0.61 fof(f379,definition,(
% 0.23/0.61 sQ22_spl <=> (in(sK6_skl,singleton(sK6_skl)))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f382,plain,(
% 0.23/0.61 sQ21_spl|sQ22_spl),
% 0.23/0.61 inference(split_clause,[status(thm)],[f374,f376,f379])).
% 0.23/0.61 fof(f385,plain,(
% 0.23/0.61 ~in(sK6_skl,sK6_skl)|~sQ21_spl),
% 0.23/0.61 inference(resolution,[status(thm)],[f377,f37])).
% 0.23/0.61 fof(f387,plain,(
% 0.23/0.61 $false|~sQ21_spl),
% 0.23/0.61 inference(forward_subsumption_resolution,[status(thm)],[f385,f377])).
% 0.23/0.61 fof(f388,plain,(
% 0.23/0.61 ~sQ21_spl),
% 0.23/0.61 inference(contradiction_clause,[status(thm)],[f387])).
% 0.23/0.61 fof(f392,plain,(
% 0.23/0.61 in(sK13_skl,succ(sK14_skl))|~sQ1_spl),
% 0.23/0.61 inference(resolution,[status(thm)],[f322,f138])).
% 0.23/0.61 fof(f394,plain,(
% 0.23/0.61 $false|sQ0_spl|~sQ1_spl),
% 0.23/0.61 inference(forward_subsumption_resolution,[status(thm)],[f392,f136])).
% 0.23/0.61 fof(f395,plain,(
% 0.23/0.61 sQ0_spl|~sQ1_spl),
% 0.23/0.61 inference(contradiction_clause,[status(thm)],[f394])).
% 0.23/0.61 fof(f402,plain,(
% 0.23/0.61 in(sK13_skl,sK14_skl)|in(sK13_skl,singleton(sK14_skl))|~sQ0_spl),
% 0.23/0.61 inference(resolution,[status(thm)],[f135,f303])).
% 0.23/0.61 fof(f407,definition,(
% 0.23/0.61 sQ23_spl <=> (in(sK13_skl,singleton(sK14_skl)))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f408,plain,(
% 0.23/0.61 in(sK13_skl,singleton(sK14_skl))|~sQ23_spl),
% 0.23/0.61 inference(component_clause,[status(thm)],[f407])).
% 0.23/0.61 fof(f410,plain,(
% 0.23/0.61 sQ1_spl|sQ23_spl|~sQ0_spl),
% 0.23/0.61 inference(split_clause,[status(thm)],[f402,f137,f407,f134])).
% 0.23/0.61 fof(f413,plain,(
% 0.23/0.61 ~in(sK13_skl,succ(sK13_skl))|~sQ2_spl|sQ0_spl),
% 0.23/0.61 inference(forward_demodulation,[status(thm)],[f141,f136])).
% 0.23/0.61 fof(f464,plain,(
% 0.23/0.61 ~succ(sK6_skl)=succ(sK6_skl)|sK6_skl=sK6_skl),
% 0.23/0.61 inference(paramodulation,[status(thm)],[f273,f372])).
% 0.23/0.61 fof(f465,definition,(
% 0.23/0.61 sQ25_spl <=> (succ(sK6_skl)=succ(sK6_skl))),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f467,plain,(
% 0.23/0.61 ~succ(sK6_skl)=succ(sK6_skl)|sQ25_spl),
% 0.23/0.61 inference(component_clause,[status(thm)],[f465])).
% 0.23/0.61 fof(f468,definition,(
% 0.23/0.61 sQ26_spl <=> (sK6_skl=sK6_skl)),
% 0.23/0.61 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.23/0.61 fof(f471,plain,(
% 0.23/0.61 ~sQ25_spl|sQ26_spl),
% 0.23/0.61 inference(split_clause,[status(thm)],[f464,f465,f468])).
% 0.23/0.61 fof(f472,plain,(
% 0.23/0.61 $false|sQ25_spl),
% 0.23/0.61 inference(trivial_equality_resolution,[status(thm)],[f467])).
% 0.23/0.61 fof(f473,plain,(
% 0.23/0.61 sQ25_spl),
% 0.23/0.61 inference(contradiction_clause,[status(thm)],[f472])).
% 0.23/0.61 fof(f589,plain,(
% 0.23/0.61 ![X0]: (in(X0,succ(X0)))),
% 0.23/0.61 inference(resolution,[status(thm)],[f342,f224])).
% 0.23/0.61 fof(f591,plain,(
% 0.23/0.61 $false|~sQ2_spl|sQ0_spl),
% 0.23/0.61 inference(backward_subsumption_resolution,[status(thm)],[f413,f589])).
% 0.23/0.61 fof(f600,plain,(
% 0.23/0.61 ~sQ2_spl|sQ0_spl),
% 0.23/0.61 inference(contradiction_clause,[status(thm)],[f591])).
% 0.23/0.61 fof(f617,plain,(
% 0.23/0.61 ![X0]: (~singleton(sK14_skl)=singleton(X0)|sK13_skl=X0|~sQ23_spl)),
% 0.23/0.61 inference(resolution,[status(thm)],[f408,f51])).
% 0.23/0.61 fof(f760,plain,(
% 0.23/0.61 sK13_skl=sK14_skl|~sQ23_spl),
% 0.23/0.61 inference(equality_resolution,[status(thm)],[f617])).
% 0.23/0.61 fof(f761,plain,(
% 0.23/0.61 sQ2_spl|~sQ23_spl),
% 0.23/0.61 inference(split_clause,[status(thm)],[f760,f140,f407])).
% 0.23/0.61 fof(f762,plain,(
% 0.23/0.61 $false),
% 0.23/0.61 inference(sat_refutation,[status(thm)],[f143,f144,f145,f172,f174,f206,f208,f216,f218,f232,f234,f382,f388,f395,f410,f471,f473,f600,f761])).
% 0.23/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.65 % Elapsed time: 0.152354 seconds
% 0.23/0.65 % CPU time: 0.724622 seconds
% 0.23/0.65 % Total memory used: 110.696 MB
% 0.23/0.65 % Net memory used: 109.353 MB
%------------------------------------------------------------------------------